Answer: 707m/s
Explanation:
The formulae for the thermal speed (Vrms) is given below as
Vrms =√3KT/m
K, T and m are all constants which implies that
Vrms is proportional to the square root of temperature.
That's (Vrms)1/√T1 = (Vrms)2/√T2
(Vrms)1 = 0.5km/s, T1 = 100°c, (Vrms)2 =?, T2 = 200°c
By substituting we have that
0.5/√100 = (Vrms)2/√200
By cross multiplication
0.5×√200 = (Vrms)2×√100
0.5 × √200 = (Vrms)2 × 10
(Vrms)2 = (0.5 × √200)/10
(Vrms)2 = 0.707 km/s.
By converting to m/s, we multiply 0.707 km/s by 1000
(Vrms)2 = 0.707×1000 = 707 m/s
The velocity of the gas at a temperature of 200°C is 563 m/s.
The rms velocity (v) is directly proportional to the square root of temperature(T).
v = k√T
When T = 100°C = 373 K, v = 0.5 km/s, hence:
0.5 = k√373
k = 0.5/√373
For temperature of 200°C, T = 473:
v = (0.5/√373) * √473 = 0.563 km/s = 563 m/s
The velocity of the gas at a temperature of 200°C is 563 m/s.
Find out more on rms at: https://brainly.com/question/9605032
